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Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation

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Abstract

The new (2+1)-dimensional generalized KdV equation which exists the bilinear form is mainly discussed. We prove that the equation does not admit the Painlevé property even by taking the arbitrary constant a=0. However, this result is different from Radha and Lakshmanan’s work. In addition, based on Hirota bilinear method, periodic wave solutions in terms of Riemann theta function and rational solutions are derived, respectively. The asymptotic properties of the periodic wave solutions are analyzed in detail.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yi Zhang, Yang Song & Wei-Wei Wei

  2. Jinhua Vocational and Technique College, Jinhua, 321007, China

    Li Cheng & Jian-Ya Ge

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  1. Yi Zhang
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  2. Yang Song
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  3. Li Cheng
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  4. Jian-Ya Ge
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  5. Wei-Wei Wei
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Correspondence to Yi Zhang.

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Zhang, Y., Song, Y., Cheng, L. et al. Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation. Nonlinear Dyn 68, 445–458 (2012). https://doi.org/10.1007/s11071-011-0228-7

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  • DOI: https://doi.org/10.1007/s11071-011-0228-7

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